The solution given to the problem in Set 3 is confusing for me. The sentences with ** to be exact.Problem
**If a system does -4.9 Joules of work against non-conservative forces**
while gravity which is the only
** conservative force acting on the system, does -9 J of work on the system**,
then what is the change in the KE of the system?
The correct statement of the problem should have been
If a system does 4.9 Joules of work against non-conservative forces**
while gravity which is the only conservative force acting on the system, does 9 J of work on the system.
The given solution should make sense in terms of this problem statement.
Solution
**The system does 4.9 Joules of work against non-conservative forces**.
**Since gravity does 9 J of work on the system, the system does - 9 J of work against gravity, thereby changing its gravitational PE by -9 J**.
* Since `dWnoncons + `dPE + `dKE = 0, we see that
* `dKE = - 4.9 J - -9 J = 4.1 J
Looking at the situation in an equivalent but slightly different way, we see that the system does total work -4.1 J.
* If the total work done by the system is positive, the energy must come from the kinetic energy of the system.
* If the total work done by the system is negative, then KE is in fact added to the system.
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The problem was apparently stated with the wrong signs on the two quantities.
In the expression
`dWnoncons + `dPE + `dKE = 0
of energy conservation the quantity `dWnoncons is what I sometimes refer to in notes as `dWnonconsBY, the work done BY the system against nonconservative forces. This quantity is equal and opposite to `dWnonconsON, which is the net work done ON the system by nonconservative forces. The other expression of energy conservation is
`dWnonconsON = `dPE + `dKE,
and since `dWnonconsON and `dWnonconsBY are equal and opposite, these two expressions of the law are easily seen to be consistent.